Surveying and Navigation, with a Preliminary Treatise on Trigonometry and MensurationVan Antwerp, Braggs & Company, 1864 - 490 páginas |
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Página 23
... sides and three angles . If three parts are given , one being a side , the re- maining parts can be computed . If the three angles only are given , the triangle is indeterminate , since an infinite number of similar triangles will ...
... sides and three angles . If three parts are given , one being a side , the re- maining parts can be computed . If the three angles only are given , the triangle is indeterminate , since an infinite number of similar triangles will ...
Página 34
... side of the one equal to two angles and the included side of the other , each to each , and are therefore equal in all their parts . Hence , OR , opposite the angle OCR , is equal to OR ' , opposite the equal angle OCR ' . Since OR is ...
... side of the one equal to two angles and the included side of the other , each to each , and are therefore equal in all their parts . Hence , OR , opposite the angle OCR , is equal to OR ' , opposite the equal angle OCR ' . Since OR is ...
Página 47
... side adjacent to the right angle is equal to the sine of the opposite angle multiplied by the hypotenuse . 2. The sine of either acute angle is equal to the opposite side divided by the hypotenuse . Since the angles P and B are ...
... side adjacent to the right angle is equal to the sine of the opposite angle multiplied by the hypotenuse . 2. The sine of either acute angle is equal to the opposite side divided by the hypotenuse . Since the angles P and B are ...
Página 48
... side adjacent to the right angle is equal to the co - sine of the adjacent acute angle multiplied by the hypot- enuse . 4. The co - sine of either acute angle is equal to the adja- cent side divided by the hypotenuse . PH PN :: HB NL ...
... side adjacent to the right angle is equal to the co - sine of the adjacent acute angle multiplied by the hypot- enuse . 4. The co - sine of either acute angle is equal to the adja- cent side divided by the hypotenuse . PH PN :: HB NL ...
Página 49
... side divided by the opposite side . BH : BT :: BP : BQ , or p 1 :: h : sec B. PH : PN :: PB : PL , or b : 1 :: h : sec P. p = h sec B h sec B ( 9 ) ( 10 ) p b - h sec P h sec P b 9. Either side adjacent to the right angle is equal to ...
... side divided by the opposite side . BH : BT :: BP : BQ , or p 1 :: h : sec B. PH : PN :: PB : PL , or b : 1 :: h : sec P. p = h sec B h sec B ( 9 ) ( 10 ) p b - h sec P h sec P b 9. Either side adjacent to the right angle is equal to ...
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Términos y frases comunes
a. c. log ABCD adjacent angles adjacent sides altitude angle is equal arc increases base line C₁ chains clamp co-sine compass cosec Cotang denote departure diameter difference of level divided east escribed circles Examples feet field notes Find the angle find the area formulas frustum given side height hence horizontal hypotenuse included angle increases from 90 instrument intersection latitude links dist logarithm longitude M.
M. Cosine M.
M. Sine mantissa meander miles minus needle negative number corresponding offsets opposite angle parallel sailing parallelogram perpendicular plane plane sailing positive quarter section corner radius rhumb line right angle sailing secant ship side adjacent sin A sin solar compass spherical triangle stake standard parallel station survey surveyor Tang tangent telescope trapezoid variation vernier versed-sine vertex vertical Willamette Meridian
Pasajes populares
Página 110 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Página 34 - If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal.
Página 258 - All the corners marked in the surveys, returned by the surveyor general, or by the surveyor of the lands south of the state of Tennessee, respectively, shall be established as the proper corners of sections, or subdivisions of sections, which they were intended to designate ; and the corners of half and quarter sections, not marked on said surveys, shall be placed as nearly as possible equidistant from those two corners which stand on the same line.
Página 22 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 19 - To Divide One Number by Another, Subtract the logarithm of the divisor from the logarithm of the dividend, and obtain the antilogarithm of the difference.
Página 144 - Any angle is greater than the difference between 180° and the sum of the other two angles.
Página 124 - That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles.
Página 65 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Página 145 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Página 162 - Now, since the areas of similar polygons are to each other as the squares of their homologous sides...